The Catalan giants tried to get a deal completed last summer for Neymar, but were unable to reach an agreement with PSG before the transfer window closed.
However, according to Spanish newspaper El Confidencial, Barca are preparing to try again when the summer transfer window opens.
The report claims Bartomeu has made it clear that he is willing to sell one or two star players in order to finance a move for the 28-year-old.
Neymar left Barca in a record-breaking €222million (£200m) move to PSG in 2017, but after spending just two years in France there are reports that he is looking for an exit from Paris.
The injury-prone winger has missed long periods of each of his three seasons in the French Capital, but he has still managed to score 66 goals and provide 39 assists in 76 appearances for PSG.
And it is this deadly form in front of goal which Messi wants to be brought back to the Nou Camp.
Barcelona are facing a difficult period at the moment on and off the field.
They are currently second in La Liga and three points behind league leaders Real Madrid.
They sacked Ernesto Valverde this season and replaced him with former Real Betis coach Quique Setien.
However, this decision then saw the club’s director of football, Eric Abidal, blame Barca’s players of underperforming for Valverde.
This in turn saw Messi take the unusual action of using social media to challenge Abidal’s remarks, as he demanded the Barca chief should name the specific players he was referring to.
It was all apparently resolved after Abidal and Bartomeu held a two-hour meeting, in which the president decided the former Barca defender would stay in his job.
Bringing Neymar back to the club would go a long way to pleasing Messi, who has yet to create the same relationship with Antoine Griezmann, that he had with the Brazilian.
The France international has scored 12 goals in 32 appearances in all competitions for Barca this season.
Barcelona are currently without striker Luis Suarez who is expected to miss the rest of the season after having surgery on his knee.
In addition to this winger Ousmane Dembele is expected to be on the sidelines for at least six months after he went under the knife on Tuesday to repair a hamstring tear.
And while Barca mull over their summer plans to bring Neymar back their immediate attention will be on finding an emergency replacement for Dembele.